English
Hindi

Question

Download Solution PDF

Find the angle between the vectors

Answer (Detailed Solution Below)

Option 3 :
Free Tests
View all Free tests >
Free
Agniveer Navy SSR Full Test - 01
100 Qs. 100 Marks 60 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept:

If  are two vectors then 

Note: If vectors  are perpendicular to each other then 

Calculation:

Given: 

Let θ be the angle between the vector 

⇒ 

We know that, 

⇒ 

⇒ 1 = 3 cos θ 

⇒  

⇒ 

Hence, option 3 is correct.

Download Solution PDF
Latest Indian Navy Agniveer SSR Updates

Last updated on Jun 20, 2025

-> The Indian Navy SSR Agniveeer Merit List has been released on the official website.

-> The Indian Navy Agniveer SSR CBT Exam was conducted from 25th to 26th May 2025.

->The application window was open from 29th March 2025 to 16th April 2025.  

-> The Indian Navy SSR Agniveer Application Link is active on the official website of the Indian Navy.

.->Only unmarried males and females can apply for Indian Navy SSR Recruitment 2025.

-> The selection process includes a Computer Based Test, Written Exam, Physical Fitness Test (PFT), and  Medical Examination.

->Candidates Qualified in 10+2 with Mathematics & Physics from a recognized Board with a minimum 50% marks in aggregate can apply for the vacancy.

-> With a salary of Rs. 30,000, it is a golden opportunity for defence job seekers.

-> Candidates must go through the Indian Navy SSR Agniveer Previous Year Papers and Agniveer Navy SSR mock tests to practice a variety of questions for the exam.

Exams Tests Super Practice

More Scalar and Vector Product Questions

Q1.The vectors \(\rm \vec a, \vec b\ and\ \vec c\) are of the same length. If taken pairwise they form equal angles. If \(\rm \vec a=̂ i+̂ j\ and \ \vec b=̂ j+̂ k,\) then what can \(\vec c\) be equal to?  I. î + k̂  II. \(\rm \frac{-\hat i+4\hat j-\hat k}{3}\) Select the correct answer using the code given below. 
Q2.Let θ be the angle between two unit vectors \(\rm \vec a\ and\ \vec b. \ if\ \vec a+2\vec b\) is perpendicular to \(\rm 5\vec a-4\vec b\) then what is cos θ + cos 2θ equal to?
Q3.For what value of the angle between the vectors \(\rm \vec a\ and \ \vec b\) is the quantity \(\rm |\vec a\times \vec b|+\sqrt3|\vec a.\vec b|\) maximum? 
Q4.What is 3α + 2β equal to if (2î + 6ĵ + 27k̂) × (î + αĵ + βk̂) is a null vector?
Q5.Three vectors \(\vec{a}, \vec{b}\) and \(\vec{c}\) are such that \(|\vec{a}|=3,|\vec{b}|=4,|\vec{c}|=5\) and each of these is perpendicular to the sum of the other two. What is \(|\vec{a}+\vec{b}+\vec{c}|\) ?
Q6.If \(\vec{a}=2 \hat{i}+5 \hat{j}+3 \hat{k}\) , \(\vec{b}=3 \hat{i}+3 \hat{j}+6 \hat{k}\) and \(\vec{c}=2 \hat{i}+7 \hat{j}+4 \hat{k}\), then \(|(\vec{a}-\vec{b}) \times(\vec{c}-\vec{a})|\) is
Q7.If \(\hat{a}\) and \(\hat{b}\) are unit vectors, and the angle between them is θ, then \(\sin \frac{\theta}{2}\) is
Q8.If \(\vec{a}, \vec{b}, \vec{c}\) are unit vectors such that \(\vec{a} \times(\vec{b} \times \vec{c})=\frac{1}{2} \vec{b}\), then the angle which \(\vec{a}\) makes with \(\vec{c}\) is
Q9.Vector \(\rm \vec A\) and \(\rm \vec B\) are parallel, then:
Q10.If \(\vec{a}\) and \(\vec{b}\) are unit vectors and θ is angle between them, then \(\frac{|\vec{a}-\vec{b}|}{2}\) is:

More Vector Algebra Questions

Q1.The vectors \(\rm \vec a, \vec b\ and\ \vec c\) are of the same length. If taken pairwise they form equal angles. If \(\rm \vec a=̂ i+̂ j\ and \ \vec b=̂ j+̂ k,\) then what can \(\vec c\) be equal to?  I. î + k̂  II. \(\rm \frac{-\hat i+4\hat j-\hat k}{3}\) Select the correct answer using the code given below. 
Q2.Let ABCDEF be a regular hexagon. If \(\rm \vec{AD}=m \vec {BC}\ and\ \vec {CF}=n\vec {AB}\) then what is mn equal to 
Q3.Let θ be the angle between two unit vectors \(\rm \vec a\ and\ \vec b. \ if\ \vec a+2\vec b\) is perpendicular to \(\rm 5\vec a-4\vec b\) then what is cos θ + cos 2θ equal to?
Q4.For what value of the angle between the vectors \(\rm \vec a\ and \ \vec b\) is the quantity \(\rm |\vec a\times \vec b|+\sqrt3|\vec a.\vec b|\) maximum? 
Q5.What is 3α + 2β equal to if (2î + 6ĵ + 27k̂) × (î + αĵ + βk̂) is a null vector?
Q6.A vector \(\rm \vec{a}=\alpha \hat{i}+2 \hat{j}+\beta \hat{k}(\alpha, \beta \in {R}) \) lies in the plane of the vectors, \(\rm \vec{b}=\hat{i}+\hat{j}\) and \(\rm \vec{c}=\hat{i}-\hat{j}+4 \hat{k}\). If \(\rm \vec{a}\) bisects the angle between \(\rm \vec{b}\) and \(\rm \vec{c}\), then
Q7.The vector equation of the plane passing through the intersection of the planes \(\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=1\) and \(\vec{r} \cdot(\hat{i}-2 \hat{j})=-2\) and the point (1, 0, 2) is:
Q8.Let ABC be a triangle such that \(\overrightarrow{B C}=\vec{a}, \overrightarrow{C A}=\vec{b}, \overrightarrow{A B}=\vec{c},|\vec{a}|=6 \sqrt{2},|\vec{b}|=2 \sqrt{3}\) and \(\vec{b} \cdot \vec{c}=12\) Consider the statements : \(\text { (S1): }|(\vec{a} \times \vec{b})+(\vec{c} \times \vec{b})|-|\vec{c}|=6(2 \sqrt{2}-1)\) \(\text { (S2): } \angle A C B=\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\) Then
Q9.Let a unit vector which makes an angle of 60° with 2î + 2ĵ - k̂ and an angle of 45° with î - k̂ be \(\vec{C}\). Then \(\vec{C}+ \left(-\frac{1}{2}\hat{i} + \frac{1}{3\sqrt{2}}\hat{j} - \frac{\sqrt{2}}{3}\hat{k}\right)\) is:
Q10.If a̅, b̅, c̅, d̅ are the position vectors of the points A, B, C, D, respectively, such that no three of them are collinear and a̅ + c̅ = b̅ + d̅. then the quadrilateral ABCD is: 
Suggested Test Series
View All >
General Knowledge for All Defence Exams
317 Total Tests with 3 Free Tests
Start Free Test
NCERT XI-XII Physics Foundation Pack Mock Test
323 Total Tests with   5 Free Tests
Start Free Test

Indian Navy Agniveer SSR Important Links

Admit CardEligibility CriteriaResultSyllabus and Exam PatternCut OffBooks

More Mathematics Questions

Q1.If cosec θ + cot θ = p, then \(\rm\frac{p^2-1}{p^2+1}\) equal:
Q2.In a binomial distribution, if the mean is 6 and the standard deviation is √2, then what are the values of the parameters n and p respectively?
Q3.Three perfect dice D1, D2 and D3 and are rolled. Let x, represent the numbers on D1, D2 and D3 respectively. What is the number of possible outcomes such that x < y < z?
Q4.Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?
Q5.The occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?
Q6.Two perfect dice are thrown. What C is the probability that the sum of the numbers on the faces is neither 9 nor 10?
Q7.Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?
Q8.A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?  
Q9.The mean of the series x1, x2...xn is x̅ If xn is replaced by k, then what is the new mean?
Q10.Let \(\rm \Sigma_{i=1}^9x_i^2=885\) If M is the mean and σ is the standard deviation of  x1, x2, x3.....x9 then what is the value of M2 + σ2?
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti earning app teen patti yas teen patti master plus teen patti royal